Finely chop the chicken. In a small bowl stir together the soy sauce and pepper. Set aside.
Pour 1 tablespoon cooking oil into a wok or large skillet. Preheat over medium heat. Add eggs. Lift and tilt the wok to form a thin sheet of egg. Cook, without stirring, about 2 minutes or just until set. Slide the egg sheet onto a cutting board. Use a knife to finely shred the cooked egg. Set aside.
Pour 1 tablespoon cooking oil into the wok or skillet. (Add more oil as necessary during cooking.) Preheat over medium-high heat. Stir-fry garlic in the hot oil for 15 seconds. Add the green onions and, if using, the sliced fresh mushrooms; stir-fry about 1-1/2 minutes or until crisp-tender. Remove vegetables from the wok. Add the chicken to the wok. Stir-fry for 2 to 3 minutes or until no pink remains. Remove chicken from the wok.
Add the cooked rice to the wok. Stir-fry for 2 to 3 minutes or until lightly browned. Drizzle the soy sauce mixture over the rice. Return the cooked vegetables and chicken to the wok. Add the shredded egg and thawed peas. Cook and stir until well mixed and heated through. Carefully stir in enoki mushrooms, if using. Serve immediately. Makes 4 servings.